Groupe d’études et de recherche en analyse des décisions

Robust stochastic games and systemic risk

Sebastian Jaimungal University of Toronto, Canada

Interbank borrowing and lending may induce systemic risk into financial markets. To incorporate this effect, log-monetary reserves must be coupled. When, banks borrow/lend from/to a central bank, and they optimize their cost of borrowing and lending in a stochastic game setting, Carmona et. al. (2015) show that market stability can be increased. Their results follow from a specific modelling framework. All models, however, have error in them, and here we account for model uncertainty (also known as ambiguity aversion) by recasting the problem as a robust stochastic game. By proving a robust variation of the stochastic Pontryagin maximum principle, we succeed in providing a strategy which leads to a Nash equilibria for the finite game, and also study the mean-field game limit. We further prove that an \(\epsilon\)-Nash equilibrium exists, and a verification theorem is shown to hold for more general convex-concave cost functions. Moreover, we show that when firms are ambiguity-averse, default probabilities can be reduced relative to their ambiguity-neutral counterparts.

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